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Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…

Brain decoding, aiming to identify the brain states using neural activity, is important for cognitive neuroscience and neural engineering. However, existing machine learning methods for fMRI-based brain decoding either suffer from low…

The Dynamic Mode Decomposition (DMD) is a Koopman-based algorithm that straightforwardly isolates individual mechanisms from the compound morphology of direct measurement. However, many may be perplexed by the messages the DMD structures…

In this paper, deep neural network (DNN) is integrated with spatial modulation-orthogonal frequency division multiplexing (SM-OFDM) technique for end-to-end data detection over Rayleigh fading channel. This proposed system directly…

Dynamic Mode Decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental characteristics of turbulence and is closely related to Koopman…

Spiking neurons can perform spatiotemporal feature detection by nonlinear synaptic and dendritic integration of presynaptic spike patterns. Multicompartment models of non-linear dendrites and related neuromorphic circuit designs enable…

Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail…

We introduce the optimized dynamic mode decomposition algorithm for constructing an adaptive and computationally efficient reduced order model and forecasting tool for global atmospheric chemistry dynamics. By exploiting a low-dimensional…

Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD) and its generalization, the extended-DMD (EDMD), are…

The spatial attention mechanism has been widely used to improve object detection performance. However, its operation is currently limited to static convolutions lacking content-adaptive features. This paper innovatively approaches from the…

This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential…

Mode decomposition is a prototypical pattern recognition problem that can be addressed from the (a priori distinct) perspectives of numerical approximation, statistical inference and deep learning. Could its analysis through these combined…

We introduce a new class of multilevel, adaptive, dual-space methods for computing fast convolutional transforms. These methods can be applied to a broad class of kernels, from the Green's functions for classical partial differential…

Effective and powerful methods for denoising real electrocardiogram (ECG) signals are important for wearable sensors and devices. Deep Learning (DL) models have been used extensively in image processing and other domains with great success…

Gesture recognition based on surface electromyographic signal (sEMG) is one of the most used methods. The traditional manual feature extraction can only extract some low-level signal features, this causes poor classifier performance and low…

Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…

Motor imagery (MI) based brain-computer interfaces (BCIs) hold significant potential for assistive technologies and neurorehabilitation. However, the precise and efficient decoding of MI remains challenging due to their non-stationary…

This paper develops data-driven methods to identify eigenfunctions of the Koopman operator associated to a dynamical system and subspaces that are invariant under the operator. We build on Extended Dynamic Mode Decomposition (EDMD), a…

Inspired by the facts that retinal cells actually segregate the visual scene into different attributes (e.g., spatial details, temporal motion) for respective neuronal processing, we propose to first decompose the input video into…

We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator. The algorithms act on data…